2013 AMC 10A Problem 10

Question

A flower bouquet contains pink roses, red roses, pink carnations, and red carnations. One third of the pink flowers are roses, three fourths of the red flowers are carnations, and six tenths of the flowers are pink. What percent of the flowers are carnations?

15

30

40

60

70

Answer: E

Concepts:fraction percentage

Difficulty rating: 1280

Small hint:

Break the bouquet into pink carnations and red carnations

Big hint:

Use the given fractions of pink and red flowers separately

Solution:

Let the total number of flowers be

x.

There are

0.6x

pink flowers and

0.4x

red flowers.

Then there are

\dfrac{1}{3} \cdot 0.6x = 0.2x

pink roses, which means there are

0.4x

pink carnations.

There are also

\dfrac{3}{4} \cdot 0.4x = 0.3x

red carnations. This means there are

0.3x + 0.4x = 0.7x

carnations. This is

70\%

of the total flowers.

Thus, E is the correct answer.